The final growth step, road-influenced
growth, is determined by the existing transportation infrastructure as
well as the most recent urbanization done under steps i,
ii and iii. With
a probability defined by breed_coefficient,
newly urbanized cells (at time t+1) are selected, and the existence
of a road is sought in their neighborhoods. If a road is found within
a given maximal radius (determined by road_gravity_coefficient)
of the selected cell, a temporary urban cell is placed at the point on
the road that is closest to the selected cell. Next, this temporary urban
cell conducts a random walk along the road (or roads connected to the
original road) where the number of steps is determined by the parameter
dispersion_coefficient.
The final location of this temporary urbanized cell is then considered
as a new urban spreading nucleus. If a neighboring cell to the temporary
urbanized cell (on the road) is available for urbanization, it will happen
(randomly picked among possible candidates). If two adjacent cells to
this newly urbanized cell are also available for urbanization it will
happen (randomly picked among candidates). Thus the creation of the temporary
urbanized cell on the road is defined by

where (i,j) are road cells neighboring (k,l).
If we define the location of the temporary urbanized cell at the end of
the random walk by (p,q), the new adjacent urban spreading center
will be defined by

where (i,j) and (k,l) belong to the
nearest neighborhood of (p,q). Note how this step is similar to
notation 3.

The four steps above are collectively referred to as a
road trip. Each attempt to select a newly urbanized pixel to move
to a road is a new road trip. The number of attempted road trips in any
given growth cycle is determined by the breed_coefficient.

Road-Influenced Growth:F(breed_coefficient, road_gravity_coefficient,
dispersion_coefficient, slope_coefficient)
{ for (p <=
breed_coefficient) { road_gravity
= value which is a function of
image size and road_gravity_coefficientmax_search
= maximum distance, determined by road_gravity,
for which a road pixel is searched (i,j)
= randomly selected pixel, urbanized within the current
growth cycle road_found
= search outward from (i,j), up to max_search,
for a road pixel if
(road_found) {
walk
along the road, in randomly selected directions,
for a number of steps determined by
the road_value and the dispersion_coefficientif
(a neighboring pixel is available for urbanization) (i,j)
neighbor = urban if
(two neighbors of the newly urban pixelare
available for urbanization) two
urban pixel neighbors = urban
} } } end road-influenced growth